Solve for x for 0 ≤ x < 2 π. tanxsinx - tanx = 0

Let's solve this

We need to accept solutions in the given interval 0 ≤ x < 2 pi

tanx * sinx - tanx = 0 First we pull out tanx in front of the bracket and get

=> tanx (sinx - 1) = 0 now we interpret product and get

tanx = 0 or sinx - 1 = 0

When tanx = 0 = > angle is x1=0

sinx - 1 = 0 = > sinx = 1 When sinx = 1 then angle is x2 = pi/2

The solutions are inside given interval 0 ≤ x < 2 pi and we accept it.

The correct answer is (x1, x2) = (0, pi/2)

Good luck!